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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 401–417 (Mi tvp723)  

A contribution to the theory of aproximately mindmax detecting of a vector signal in a Gaussian noise

Yu. V. Linnika, Yu. V. Prokhorovb, O. V. Shalaevskiia

a Leningrad
b Moscow

Abstract: In a normal size $N$ sample of independent indentically distributed variables $X_i\in\mathbf N(\xi,\Sigma)$ with covariance matrix unknown, the hypothesis $H_0\colon\xi=0$ againts $H_\delta\colon N\xi^T\Sigma^{-1}\xi\ne\delta$ is tested.
The well known Hotelling test $(T^2)$ is proved to be approximately minimax with considerable accuracy in the following sense: for all randomized level $\alpha$ tests $\Phi$ and a fixed positive $\delta$ we have:
$$ \sup_\Phi\inf_{\theta\in H_\delta}\mathbf E_\theta\Phi-\inf_{\theta\in H_\delta}\mathbf E_\theta(T^2)=O(\exp c_1N^{1/4}\ln N) $$
with $\theta=(\xi,\Sigma),$ $c_1>0$.

Full text: PDF file (812 kB)

English version:
Theory of Probability and its Applications, 1967, 12:3, 347–363

Bibliographic databases:

Received: 20.04.1967

Citation: Yu. V. Linnik, Yu. V. Prokhorov, O. V. Shalaevskii, “A contribution to the theory of aproximately mindmax detecting of a vector signal in a Gaussian noise”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 401–417; Theory Probab. Appl., 12:3 (1967), 347–363

Citation in format AMSBIB
\Bibitem{LinProSha67}
\by Yu.~V.~Linnik, Yu.~V.~Prokhorov, O.~V.~Shalaevskii
\paper A~contribution to the theory of aproximately mindmax detecting of a~vector signal in a~Gaussian noise
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 401--417
\mathnet{http://mi.mathnet.ru/tvp723}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=215423}
\zmath{https://zbmath.org/?q=an:0183.22102}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 347--363
\crossref{https://doi.org/10.1137/1112047}


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